@Jgav – I’ll put some more thought into this later on, but for now…
I can see the swings in your initial thoughts, but about everything else in the photo?
(Do you want/need to keep the shed, tool store, goal post, etc.)
”Patio near the doors from the house is too narrow to put any outdoor furniture so it’s tucked down away from the house and so we don’t use it as much.”
OK, so if I’m reading the layouts right…
The area behind the wheelie bin is in front of a fence, not in front of the house?
”I hate that the steps point up to an ugly shed which is right in the middle of where we look out of our house.”
Any chance of some photos showing the rear doors/windows and the current view looking out?
Similarly, any chance of some photos from an upstairs window looking down?
(As the fish eye photo is tricky to line up with the plans.)
”I also hate the massive fir in the garden behind us which blocks all light, but I don’t think we can do anything about that.”
No harm in asking your neighbour can you trim it for them.
(Especially, if you are prepared to supply/pay for a tree surgeon.)
As most people when faced with a problem tree in their garden just leave it there. 
Our tree surgeon usually gets more work from neighbours who see him working in our garden.
Do you have access to the front of the house?
Are you hoping that all the soil removed when you extend the patio into the current raised area will be reallocated into another part of the garden, or will you need to get it removed?
By chance, I’ve got a couple of photos from our garden re-design and we also moved the stairs.
(From the middle of the patio to one side.)
Before:
(Well, technically ‘during’.)

After:
(With an extra hedge in front of where the stairs used to be.)

This made a HUGE difference in how we used the patio and we love sitting/eating outside. 
And whilst it is definitely worth getting the garden you want, don’t underestimate the work.
(We used friends working for food & drink during the day and curry & beer at night! )

”Tree hasn’t blown over, just grown like that. It’s a sick apple tree and I want rid.”
Understand getting rid of that tree, but are you removing all the others at the back too?
I was impressed with the three trees I bought in 2020, as they were a decent size to start with.

So maybe consider changing trees rather than not having any at all.
Good luck, Paul. 